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# Algebra
-*Note: Most of the definitions and notation in the section are based on [rudin] or [meserve].*
+*Note: Most of the definitions and notation in the section are based on [^rudin] or [^meserve].*
+----------- ----------------- -------------- --------------- ---------- --------------------- --------
Name Symbol Pos. Integers? Pos. Rationals? Rationals? Reals (wrt Pos Int.)? Complex?
----- ----------------- -------------- --------------- ---------- --------------------- --------
+----------- ----------------- -------------- --------------- ---------- --------------------- --------
addition $a + b$ Y Y Y Y Y
+
product $a\times b$ Y Y Y Y Y
+
subtraction $a-b$ N N Y Y Y
+
division $\frac{a}{b}$ N Y Y Y Y
+
power $a^b$ Y Y Y Y Y
+
root $\sqrt{\text{a}}$ N N N Y Y
----- ----------------- -------------- --------------- ---------- --------------------- --------
+----------- ----------------- -------------- --------------- ---------- --------------------- --------
Table: Closure of binary operators on given sets of numbers
## Definitions
involution
- to raise a number to a given power
+: to raise a number to a given power
evolution
- to take a given root of a number
+: to take a given root of a number
associative
- $(a+b)+c=a+(b+c)$
+: $(a+b)+c=a+(b+c)$
-comutative
- $a+b=b+c$
+commutative
+: $a+b=b+c$
distributive
- $(a+b)c=ac+bc$
+: $(a+b)c=ac+bc$
-[^rudin] **Principles of Mathematical Analysis (3rd ed)**, by Walter Rudin. McGraw-Hill, 1976
+[^rudin]: **Principles of Mathematical Analysis (3rd ed)**, by Walter Rudin. McGraw-Hill, 1976
-[^meserve] **Fundamental Concepts of Algebra**, by Bruce Meserve.
+[^meserve]: **Fundamental Concepts of Algebra**, by Bruce Meserve.